Spectral Informed Mamba for Robust Point Cloud Processing

State Space Models (SSMs) have shown significant promise in Natural Language Processing (NLP) and, more recently, computer vision. This paper introduces a new methodology that leverages Mamba and Masked Autoencoder (MAE) networks for point-cloud data in both supervised and selfsupervised learning. We propose three key contributions to enhance Mamba's capability in processing complex pointcloud structures. First, we exploit the spectrum of a graph Laplacian to capture patch connectivity, defining an isometry-invariant traversal order that is robust to viewpoints and captures shape manifolds better than traditional 3D grid-based traversals. Second, we adapt segmentation via a recursive patch partitioning strategy informed by Laplacian spectral components, allowing finer integration and segment analysis. Third, we address token placement in MAE for Mamba by restoring tokens to their original positions, which preserves essential order and improves learning. Extensive experiments demonstrate the improvements that our approach brings over state-of-the-art baselines in classification, segmentation, and few-shot tasks. The implementation is available at: https://github.com/ AliBahri94/SI-Mamba.git.